therefore are most of the mechanisms in common use. To the thorough, thoughtful mechanician who looks at his work as a serious matter, a scientific investigation of the Kinematics of Machinery will in this respect be specially valuable. It will relieve him of the minute and often worrying search after solutions of his problems by rendering it possible for him to work systematically. The technologist too, who hitherto has scarcely made any use of Kinematics, will find in it an important assistance in understanding old machines and devising new ones. The deepening of the comprehension which must occur in such cases as these renders it certain that the remodelled science will take its share in the real end before us,—the progressive development of the machine.
If we look back over the representation I have tried to give of the way in which the subject has hitherto been treated, and of the Ideal to be aimed at, the old method appears to have no inner unity, although the scientific methods of investigation which it employs have prevented this from being generally recognised. We have, however, shown that these are only of secondary importance compared with the establishment of the special ideas and principles peculiar to the subject. This question, moreover, must at once be seen to be one which actually concerns a department of investigation belonging distinctly to the exact sciences. This being recognised, the former method must be considered insufficient and not permanently tenable, for it permits of deductions only to a limited extent, and does not make it possible to give reasons for existing phenomena.
The remodelling which has become necessary requires undisturbed adherence to clear, simple, logical principles. What, however, is to be drawn from our criticism of the system hitherto used,—what I have endeavoured to illustrate and develope by single instances,—what the philosophical sentences I have quoted bring before us in a condensed form,—we may contract into one word. So far as our special problem is concerned, the question is to make the science of machinery deductive. The study must be so formed that it rests upon a few fundamental truths peculiar to itself. The whole fabric must be reducible to their strictness and simplicity, and from them again we must be able, conversely, to develope it. Here again is a point from which the weakness of the method hitherto employed can be surveyed at a glance. Its difference from the
